Deformation response and triggering factors of the reservoir landslide–pile system based upon geographic detector technology and uncertainty of monitoring data

Abstract

Understandings of reinforcement mechanisms of landslide-stabilizing pile system are important for long-term safety of reservoir landslides installed piles. The paper proposes a framework to study deformation response and identify triggering factors for landslide–pile system by using geographic detector technology and uncertainty of monitoring data. Majiagou landslide, a representative reservoir landslide installed stabilizing and test piles, is selected as the case study. Firstly, monitoring data of monthly rainfall, variations of reservoir water level, deformation of landslide surface and piles’ head were preprocessed. The random deformation data were generated considering uncertainty of deformation monitoring data. Meanwhile, the deformation response of landslide–pile system is analyzed through studying the monitoring deformation data and random deformation data using the clustering algorithm. Finally, geographic detector technique was used to identify main triggering factors of landslide surface deformation and explore interaction types of any two factors. The uncertainty of monitoring data was used to identify the most important triggering factor. Influences of different error and uncertainty of monitoring data on the influence degrees of each factor were further discussed. The comparison with improved Apriori algorithm shows that the presented framework can intuitively measure influence degrees of each factor and analyze interaction types of any two factors. The main conclusions by studying Majiagou landslide indicate that the anti-slide performance and action range of piles gradually decrease with the increase of hydraulic cycle; the deterioration of geomaterials’ properties are the most important triggering factor leading to the deformation of landslide–pile system and the degradation of piles’ performance, supported by most random deformation groups.

Appendices

Appendix 1: The equations of distance between clusters and threshold for Clustering algorithm

The equations of distance d(j, s) between clusters j and s in Euclidean n-space is

$$d(j,s) = \sqrt {\sum\limits_{i = 1}^{n} {(x_{i} - y_{i} )^{2} } }$$

(1)

where, x_i and y_i are the coordinates of the centroids of clusters j and s.

The distance threshold C can be presented as:

$$C{ = 2}\sqrt {\frac{1}{JK}\sum\limits_{j = 1}^{J} {\sum\limits_{k = 1}^{K} {\delta_{jk}^{2} } } }$$

(2)

where, K is the total number of all input quantitative records, J is the total number of quantitative variables in cluster j, and $\delta_{jk}^{2}$ is the estimated variance of the kth quantitative variable in cluster j.

Appendix 2: The equations of the extent that factor X to explain the spatial stratified heterogeneity of property Y for geographical detector technique

Factor detector can probe the spatial stratified heterogeneity of Y and probe the extent of factor X to explain the spatial stratified heterogeneity of property Y. The extent q can be measured by:

$$\begin{aligned} & q = 1 - \frac{{\sum\nolimits_{h = 1}^{L} {N_{h} \sigma_{h}^{2} } }}{N\sigma } = 1 - \frac{SSW}{SST} \\ & SSW = \sum\limits_{h = 1}^{L} {N_{h} \sigma_{h}^{2} } , \, \quad SST = N\sigma \\ \end{aligned}$$

(3)

where, h = 1, 2, …, L is the strata (classification or partition) of variable Y or factor X; N_h and N are units of strata h and the whole region, respectively; $\sigma_{h}^{2}$ and $\sigma_{h}^{{}}$ are the variances of Y values of strata h and the whole region, respectively; SSW and SST are within sum of squares and total sum of squares.

Appendix 3: The equations of support, confidence and lift in Apriori algorithm

The support of X ⇒ Y is the frequency of occurring patterns and is defined as:

$$S_{X \Rightarrow Y} = \frac{{|T\left( {X \cup Y} \right)|}}{|T|}$$

(4)

The confidence of X ⇒ Y is defined as:

$$C_{X \Rightarrow Y} = \frac{{|T\left( {X \cup Y} \right)|}}{|T\left( X \right)|}$$

(5)

The lift of X ⇒ Y is defined as:

$$C_{X \Rightarrow Y} = {{\frac{{|T\left( {X \cup Y} \right)|}}{|T\left( X \right)|}} \mathord{\left/ {\vphantom {{\frac{{|T\left( {X \cup Y} \right)|}}{|T\left( X \right)|}} {\frac{|T\left( Y \right)|}{|T|}}}} \right. \kern-0pt} {\frac{|T\left( Y \right)|}{|T|}}}$$

(6)

In these expressions, |T(X∪Y)| is the total number of times that both itemsets X and Y are found in the transaction database T, |T(X)| is the total number of times that itemset X is found in the transaction database T, |T(Y)| is the total number of itemsets Y in the transaction database T, and |T| is the total number of records in the transaction database T.